Annotation of rpl/lapack/lapack/zlaqz1.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZLAQZ1
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAQZ1 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ZLAQZ1.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ZLAQZ1.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ZLAQZ1.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAQZ1( ILQ, ILZ, K, ISTARTM, ISTOPM, IHI, A, LDA, B,
! 22: * $ LDB, NQ, QSTART, Q, LDQ, NZ, ZSTART, Z, LDZ )
! 23: * IMPLICIT NONE
! 24: *
! 25: * Arguments
! 26: * LOGICAL, INTENT( IN ) :: ILQ, ILZ
! 27: * INTEGER, INTENT( IN ) :: K, LDA, LDB, LDQ, LDZ, ISTARTM, ISTOPM,
! 28: * $ NQ, NZ, QSTART, ZSTART, IHI
! 29: * COMPLEX*16 :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZLAQZ1 chases a 1x1 shift bulge in a matrix pencil down a single position
! 39: *> \endverbatim
! 40: *
! 41: *
! 42: * Arguments:
! 43: * ==========
! 44: *
! 45: *>
! 46: *> \param[in] ILQ
! 47: *> \verbatim
! 48: *> ILQ is LOGICAL
! 49: *> Determines whether or not to update the matrix Q
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] ILZ
! 53: *> \verbatim
! 54: *> ILZ is LOGICAL
! 55: *> Determines whether or not to update the matrix Z
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] K
! 59: *> \verbatim
! 60: *> K is INTEGER
! 61: *> Index indicating the position of the bulge.
! 62: *> On entry, the bulge is located in
! 63: *> (A(k+1,k),B(k+1,k)).
! 64: *> On exit, the bulge is located in
! 65: *> (A(k+2,k+1),B(k+2,k+1)).
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] ISTARTM
! 69: *> \verbatim
! 70: *> ISTARTM is INTEGER
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] ISTOPM
! 74: *> \verbatim
! 75: *> ISTOPM is INTEGER
! 76: *> Updates to (A,B) are restricted to
! 77: *> (istartm:k+2,k:istopm). It is assumed
! 78: *> without checking that istartm <= k+1 and
! 79: *> k+2 <= istopm
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] IHI
! 83: *> \verbatim
! 84: *> IHI is INTEGER
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[inout] A
! 88: *> \verbatim
! 89: *> A is COMPLEX*16 array, dimension (LDA,N)
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] LDA
! 93: *> \verbatim
! 94: *> LDA is INTEGER
! 95: *> The leading dimension of A as declared in
! 96: *> the calling procedure.
! 97: *> \endverbatim
! 98: *
! 99: *> \param[inout] B
! 100: *> \verbatim
! 101: *> B is COMPLEX*16 array, dimension (LDB,N)
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[in] LDB
! 105: *> \verbatim
! 106: *> LDB is INTEGER
! 107: *> The leading dimension of B as declared in
! 108: *> the calling procedure.
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in] NQ
! 112: *> \verbatim
! 113: *> NQ is INTEGER
! 114: *> The order of the matrix Q
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] QSTART
! 118: *> \verbatim
! 119: *> QSTART is INTEGER
! 120: *> Start index of the matrix Q. Rotations are applied
! 121: *> To columns k+2-qStart:k+3-qStart of Q.
! 122: *> \endverbatim
! 123: *
! 124: *> \param[inout] Q
! 125: *> \verbatim
! 126: *> Q is COMPLEX*16 array, dimension (LDQ,NQ)
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in] LDQ
! 130: *> \verbatim
! 131: *> LDQ is INTEGER
! 132: *> The leading dimension of Q as declared in
! 133: *> the calling procedure.
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[in] NZ
! 137: *> \verbatim
! 138: *> NZ is INTEGER
! 139: *> The order of the matrix Z
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] ZSTART
! 143: *> \verbatim
! 144: *> ZSTART is INTEGER
! 145: *> Start index of the matrix Z. Rotations are applied
! 146: *> To columns k+1-qStart:k+2-qStart of Z.
! 147: *> \endverbatim
! 148: *
! 149: *> \param[inout] Z
! 150: *> \verbatim
! 151: *> Z is COMPLEX*16 array, dimension (LDZ,NZ)
! 152: *> \endverbatim
! 153: *>
! 154: *> \param[in] LDZ
! 155: *> \verbatim
! 156: *> LDZ is INTEGER
! 157: *> The leading dimension of Q as declared in
! 158: *> the calling procedure.
! 159: *> \endverbatim
! 160: *
! 161: * Authors:
! 162: * ========
! 163: *
! 164: *> \author Thijs Steel, KU Leuven
! 165: *
! 166: *> \date May 2020
! 167: *
! 168: *> \ingroup complex16GEcomputational
! 169: *>
! 170: * =====================================================================
! 171: SUBROUTINE ZLAQZ1( ILQ, ILZ, K, ISTARTM, ISTOPM, IHI, A, LDA, B,
! 172: $ LDB, NQ, QSTART, Q, LDQ, NZ, ZSTART, Z, LDZ )
! 173: IMPLICIT NONE
! 174: *
! 175: * Arguments
! 176: LOGICAL, INTENT( IN ) :: ILQ, ILZ
! 177: INTEGER, INTENT( IN ) :: K, LDA, LDB, LDQ, LDZ, ISTARTM, ISTOPM,
! 178: $ NQ, NZ, QSTART, ZSTART, IHI
! 179: COMPLEX*16 :: A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
! 180: *
! 181: * Parameters
! 182: COMPLEX*16 CZERO, CONE
! 183: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), CONE = ( 1.0D+0,
! 184: $ 0.0D+0 ) )
! 185: DOUBLE PRECISION :: ZERO, ONE, HALF
! 186: PARAMETER( ZERO = 0.0D0, ONE = 1.0D0, HALF = 0.5D0 )
! 187: *
! 188: * Local variables
! 189: DOUBLE PRECISION :: C
! 190: COMPLEX*16 :: S, TEMP
! 191: *
! 192: * External Functions
! 193: EXTERNAL :: ZLARTG, ZROT
! 194: *
! 195: IF( K+1 .EQ. IHI ) THEN
! 196: *
! 197: * Shift is located on the edge of the matrix, remove it
! 198: *
! 199: CALL ZLARTG( B( IHI, IHI ), B( IHI, IHI-1 ), C, S, TEMP )
! 200: B( IHI, IHI ) = TEMP
! 201: B( IHI, IHI-1 ) = CZERO
! 202: CALL ZROT( IHI-ISTARTM, B( ISTARTM, IHI ), 1, B( ISTARTM,
! 203: $ IHI-1 ), 1, C, S )
! 204: CALL ZROT( IHI-ISTARTM+1, A( ISTARTM, IHI ), 1, A( ISTARTM,
! 205: $ IHI-1 ), 1, C, S )
! 206: IF ( ILZ ) THEN
! 207: CALL ZROT( NZ, Z( 1, IHI-ZSTART+1 ), 1, Z( 1, IHI-1-ZSTART+
! 208: $ 1 ), 1, C, S )
! 209: END IF
! 210: *
! 211: ELSE
! 212: *
! 213: * Normal operation, move bulge down
! 214: *
! 215: *
! 216: * Apply transformation from the right
! 217: *
! 218: CALL ZLARTG( B( K+1, K+1 ), B( K+1, K ), C, S, TEMP )
! 219: B( K+1, K+1 ) = TEMP
! 220: B( K+1, K ) = CZERO
! 221: CALL ZROT( K+2-ISTARTM+1, A( ISTARTM, K+1 ), 1, A( ISTARTM,
! 222: $ K ), 1, C, S )
! 223: CALL ZROT( K-ISTARTM+1, B( ISTARTM, K+1 ), 1, B( ISTARTM, K ),
! 224: $ 1, C, S )
! 225: IF ( ILZ ) THEN
! 226: CALL ZROT( NZ, Z( 1, K+1-ZSTART+1 ), 1, Z( 1, K-ZSTART+1 ),
! 227: $ 1, C, S )
! 228: END IF
! 229: *
! 230: * Apply transformation from the left
! 231: *
! 232: CALL ZLARTG( A( K+1, K ), A( K+2, K ), C, S, TEMP )
! 233: A( K+1, K ) = TEMP
! 234: A( K+2, K ) = CZERO
! 235: CALL ZROT( ISTOPM-K, A( K+1, K+1 ), LDA, A( K+2, K+1 ), LDA, C,
! 236: $ S )
! 237: CALL ZROT( ISTOPM-K, B( K+1, K+1 ), LDB, B( K+2, K+1 ), LDB, C,
! 238: $ S )
! 239: IF ( ILQ ) THEN
! 240: CALL ZROT( NQ, Q( 1, K+1-QSTART+1 ), 1, Q( 1, K+2-QSTART+
! 241: $ 1 ), 1, C, DCONJG( S ) )
! 242: END IF
! 243: *
! 244: END IF
! 245: *
! 246: * End of ZLAQZ1
! 247: *
! 248: END SUBROUTINE
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